Evaluating Impacts of a Disaster in Tokai Region of Japan:
A Dynamic Spatial CGE Model
Hiroyuki SHIBUSAWA*, Makoto YAMAGUCHI* and Yuzuru MIYATA*

1. Introduction
In this paper, we develop a dynamic spatial CGE model to evaluate theeconomic impacts of an earthquake on Tokai region in Japan. Our model ischaracterized as a decentralized economy with utility-maximizing consumers andvalue-maximizing firms in the dynamic context. Both the spatial interactions among
regions and the dynamics of regional investments are specified in this model.
A numerical simulation model is constructed under the inter-regional
inter-sectoral economy where Japan is subdivided into 47 regions. All the regions areconnected by the transportation networks. The model is calibrated for the regional
economy in Japan. By numerical simulation, we will evaluate the economic impacts ofan earthquake on Tokai region.
2. The Model
The world is subdivided by region. There are general industry (tradable goods
and non-tradable goods), transportation industry and households. The economy isendowed with primary factors, labor and capital. Labor is mobile across industries but
not regions and capital is immobile across industries and regions. Goods and factor
prices are determined in perfectly competitive regional markets. Commodity trade
between regions in the country generates demand for transportation services and unittransportation costs are endogenous. Commodities are imperfect substitutes, i.e., they
are differentiated according to region of production. The interaction of commodities
among regions is performed by transportation networks. The model is solved forrational expectation equilibrium under perfect competition and foresight.
The model is finitely set up in discrete time. I P ≡ {1, 2,L , T } denotes aplanning period index and T is the final planning period. The world is divided into ahome country and foreign country. These are subdivided by region. R denotes a*Toyohashi University of Technology, 1-1 Tempaku Toyohashi, Aichi 441-8580, Japanregional index at the home country. There are four kinds of industries, i.e. tradable
goods, non-tradable goods, transportation and distribution industries. The tradable
goods industry involves domestic and foreign trades among regions. I I denotes asector index for the tradable goods industry and I O denotes a sector index for thenon-tradable goods industry. IT is a sector index of the transportation industry and I D
is a sector index of the composite production industry. We also tractably set twoindices, I IO ≡ I I ∪ I O and I IOT ≡ I I ∪ I O ∪ IT . All regions interact with each other bytransportation networks. The transportation network is defined by nodes and links. Atransport path connecting two regions is fixed and the transport link distance isexogenously given.
3. The Decentralized Economy
The model is based on dynamic macroeconomic theory with a multi-region
and multi-sector specification. In each region, there are production and household
sectors. Commodity trade flows are linked by the Armington system. We characterize
the maximization problem of production and household sectors in this economy.
3.1 Production Sectors
Each sector of the tradable, non-tradable, transportation industries maximizes
the present value of its cash flow at each period NCitr and the asset value of industrial
capital at final period Φ iz ( ) . The sector operates with constant returns to scaletechnology. The sector chooses the optimal investment and labor employmentstrategies. The behavior of the production sector i ∈ I IOT in region r ∈ R is given asmax{ Kitr , Lrit , Xitr , Zitr }∑ ρ NC + ρ Φ ( Kt∈I Ptr
itT +1riri ,T +1),

subject to K ir,t +1 = (1 − δ i ) K itr + ∆K itr (Ζitr ) ,wherer
Drr
NCitr ≡ pitOrYi r ( K itr , Lrit , Xitr ) − wtr Lrit − ∑ p Dr
jt X jit − ∑ p jt G j ( Z jit ) .
j∈I IOj∈I IOρt ≡ 1/(1 + ρ )t −1 represents the discount factor and ρ is the positive discount rate.
Yi r ( ) is a production function of capital K itr , labor Lrit , and a vector of intermediate
input Xitr = { X 1rit ,L , X IrIOit } . The value added production function for labor and capital
is of Cobb-Douglas form, while the intensities of intermediate goods are fixed. The
asset value at final period Φ ir ( ) is a linear function of capital stock at the final period.
The capital stock K itr is accumulated by an investment function ∆K itr ( ) withconstant-returns-to-scale. It is a function of a vector of intermediate inputs for the2

investment Zitr = {Z1rit ,L , Z IrIOit } and a Leontief type technology is assumed. δ i is thedepreciation rate. The investment involves adjustment costs. G j ( ) represents anadjustment function and it has an increasing returns to scale. In those sectors, there are
two kinds of prices in each region. One is the producer’s price pitOr and another is thepurchase’s price p Drin region r . If a commodity i is tradable between region ojand region d , then the producer’s price in region o is represented by pitOo and thepurchaser’s price is represented by piDd (i ∈ I I ) . If it is non-tradable one, then two
prices have the same values and are denoted by pitDd = pitOo (i ∈ I O ) . In thetransportation sector, pitOr (i ∈ I I ) means the unit price of the transportation services
in region r . wtr is the wage rate.
After having paid wages to households, the sector has to decide to how todistribute profit and finance the investment. In this model, we follow an assumptionthat a replacement investment is financed out of retained earnings and net investment
is financed by new bonds (ref. Abel and Blanchard (1983)). Let Bitr be the number ofbonds at period t and rt r be the interest rate. The bonds are traded in the regional
market in each region. The initial number of bonds is normalized by Bir1 = K ir1 . In thiscase, the profit dividend is calculated aszrr
π itr = pitOrYi r ( K itr , Lrit , Xitr ) − ritr Bitr − wtr Lrit − ∑ p Dzj X ji − p Bit δ i K it .
j∈I IO

If the production function is of the constant returns to scale, then the dividend torhouseholds can be calculated as pBit
δ i K itr . If the net investment is financed by issuing
new bonds, it holds thatrr
rr
pBit∆Bitr = ∑ p Dr
jt G j ( Z jit ) − pBit δ i K it ,j∈I IO

where ∆Bitr is the number of new bonds issued by sector i in region r at period t .
rpBit
is the price of the new bond. Therefore the outstanding bond is given byr
Bi ,t +1 = Bitr + ∆Bitr with ∑ i∈I Bir1 = B r .
IOTIn this model, we rely on the theory of demand distinguished by place ofproduction. We assume that tradable goods are imperfect substitutes (Armington1969)1. The behavior of the sector for regional composite goods is given by (i ∈ I D )TorOjojrrDr rr
OoTor
ormax π Dit = pit YDi (Fit ) − ∑ ∑ ( pit + pilt ) Filt where pilt ≡ κ ilt ∑ plt Dlt .

{Fitr }o∈R l∈ITj∈R1The Armington approach internalizes the trade coefficients, making them sensitive to the relative
prices of goods from different origins.

3YDir ( )is a function of a vector of commodity trade flowsr
1r
Fit = {Fi1t ,L , Fi1Rrt ,L , FiI1Trt ,L , FiIRrT t } and it is of a nested CES production function withconstant returns to scale. piltTor is the transportation cost of mode l from region oto region r . Dltojr is the link distance in region r and the total distance between
origin and destination is calculated by the sum of Dltojr along with a path. The path isexogenously given by the shortest path rule. κ lit is a given unit transportation
services of mode l for goods i .
3.2 Household Sector

A representative household maximizes the utility level subject to the income
constraint. The full income consists of wage and interest on bond holdings. The
behavior of the household in region r ∈ R is given asmaxrr{C , Ai ,∆Ai }rsubject to1∑ ρ σ U (T − L , C )σ + ρ Φ (At∈I Prt

Hr
Strt

T +1r
Hr
T +1),rwtr LrSt + ∑ ritr Aitr + d tr + FAtr − ∑ pitDr Citr − ∑ pBit
∆Aitr ≥ 0 ,i∈I IOTi∈I IOi∈I IOT

Air,t +1 = ∆Aitr + Aitr (i ∈ I IOT ) and dtr ≡ ∑ π itr / N tr .
i∈I IOTU r ( ) is a Cobb-Douglas utility function at period t and it is a function of leisureTH − LrSt and a vector of consumptions Ctr = {C1rt ,L , CIrIO t } . σ is the parameter whichis related to the elasticity of intertemporal substitution. TH is the given available timeand LrSt is labor time. Aitr is the number of bond holdings per household. ∆Aitr isnew bonds issued for industrial investments. The household can get the interest income
but pay to get a new bond. FAtr is the income transfer which balances against asurplus or deficit in the foreign trade. Φ rH ( ) is the assets value at final period and it
is a linear function of a vector of bonds ATr +1 = { A1r,T +1 ,L , AIrIOT ,T +1} .
3.3 Equilibrium Conditions(1) Goods and Services Markets(a)Tradable Goods
Yi r ( K itr , Lrit , Xitr ) = ∑ ∑ Filtrd + EX it (r ∈ R, i ∈ I I )rd ∈R l∈IT

rit

EX is given export goods from region r to another country.
(b)Non-tradable Goods
Yi r ( K itr , Lrit , Xitr ) = ∑ X ijtr + Citr N tr + ∑ G j ( Z ijtr )j∈I IOTj∈I IOT(c)Transportation Services

4( r ∈ R, i ∈ I O )od( r ∈ R, i ∈ I T )Yi r ( K itr , Lrit , Xitr ) = ∑ ∑ ∑ κ jit D ordjit F jit
j∈I I o∈R d ∈R(d)Regional Composite Goods
YDir (Fitr ) = ∑ X ijtr + Citr N tr + ∑ G j ( Z ijtr ) − IM it (r ∈ R, i ∈ I D )rj∈I IOTIMritj∈I IOT

is a given total import from abroad to region r .

(2) Labor
LrSt N tr = ∑ Lrit(r ∈ R)i∈I IOT

N tr is total labor (population ) in each region.
(3) Capital∆Aitr N tr = ∆Bitr (r ∈ R, i ∈ I IOT )Aitr N tr = Bitr = K itr with Air1 N1r = Bir1 = K ir1 (r ∈ R, i ∈ I IOT )A1ri is an initial number of bond holdings of a household.
4. Numerical Application

In the simulation model, the world is subdivided into 47 regions of which
cover all prefectures of Japan. The economy is classified into 7 sectors. Generalindustry is simply divided to 3 sectors, i.e. agriculture, manufacturing industry, andservices. There are four kinds of transportation networks: road, railway, sea, and air.
Then the transportation industry is classified into 4 sectors. Each network structure,node and link, is given at each period. To fix a path between an origin and a destination,
the shortest path rule is adopted. The planning period is given as T=10. Population
growth and the technological progress are also fixed during planning periods.
Several scenarios are set to evaluate dynamic impacts of an earthquake on
Tokai region (including Shizuoka, Aichi, and Mie prefectures). Numerical results will
be shown in the meeting.

5References

Abel, A.B. and Blanchard, O. J., An Intertemporal Model of Saving and Investment,
Econometrica, Vol.51, No.3, 1983, pp.675-692.
Ciesecke, J., Explaining Regional Economic Performance: An Historical Applicationof a Dynamic Multi-Regional CGE Model, Papers in Regional Science, Vol.81,
2002, pp.247-247.
Ciesecke, J., Targeting Regional Output with State Government Fiscal Instruments: A
Dynamic Multi-Regional CGE Analysis, Australian Economic Papers, Vol.42,
2003, pp.214-223.
Kehoe, T.J., Srinivasan, T.N. and Whalley, J., Frontiers in Applied General
Equilibrium Modeling, Cambridge University Press, 2005.
Koike, A. and Ueda, T., Economic Damage Assessment of Catastrophe by using
Spatial General Computable General Equilibrium Analysis, Proceeding of the 19th
Pacific Regional Science Conference, 2005.
McGregor, P.G., Swales, K., and Yin, Y.P., Migration Equilibria in Regional
Economies: A Multi-Period CGE Analysis of an Improvement in Local Amenities,
in Recent Advances in Spatial Equilibrium Modeling, eds. Jeroen C.J.M. Van Den
Bergh, P. Nijkamp, and P.Rietveld, New York: Springer, 1995.
McKibbin ,W. and Wilcoxen, P., GCUBED: A Dynamic Multi-Sector General
Equilibrium Growth Model of the Global Economy, Brookings Discussion Papers
in International Economics, No.97, 1992.
Okuyama, Y. and Chang, S.E., Modeling Spatial and Economic Impacts of Disasters,Springer, 2004.
Shibusawa, H., Higano, Y. and Miyata, Y., A Dynamic Multi-regional CGE Model withTransportation Networks: Equilibrium and Optimality, Studies in Regional
Science, Vol.37, No.2 (in press).
Sohn, J., Kim, T.J., Hewings, J.D., Lee, J.S. and Jang, S-G, Retrofit Priority ofTransport Network Links under an Earthquake, Journal of Urban Planning &Development, 2003, pp.195-210.

6